Systems and methods for prediction of objective visual acuity based on wavefront measurements

ABSTRACT

Methods, devices, and systems for predicting an optical acuity measure of an optical system of an eye. An optical acuity measure can be predicted by determining a point spread function based on a wavefront measurement of an eye, convolving a resolution target with the point spread function to produce an image, and predicting the optical acuity measure of the optical system of the eye based on the image.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a division of U.S. patent application Ser. No.12/013,763 (Attorney Docket No. 018158-023311US), filed Jan. 14, 2008,which is a division of U.S. patent application Ser. No. 10/871,344(Attorney Docket No. 018158-023310US), filed Jun. 18, 2004, which claimspriority from U.S. Provisional Patent Application No. 60/480,237(Attorney Docket No. 018158-02330005), filed Jun. 20, 2003. The entiredisclosure of each of these applications is incorporated herein byreference for all purposes.

REFERENCE TO SEQUENCE LISTING

NOT APPLICABLE

BACKGROUND OF THE INVENTION

This invention relates to optical system analysis, and in particularprovides methods and systems for evaluating an optical acuity measure ofan individual's eye.

The visual acuity of the eye can be affected by many factors. Forexample, visual acuity can be affected by objective factors such as theoptical characteristics of the cornea and lens, as well as subjectivefactors such as light absorption and detection in the retina, and neuralprocessing in the brain. Traditionally, measuring visual acuity of thehuman eye has involved methods using eye charts. The test results fromsuch methods, however, can be subjective in nature as they involve thehuman brain's interpretation of vision, and therefore may not berepresentative of the quality of the eye's optics.

It would be desirable to have improved methods and systems that provideaccurate and objective prediction and evaluation of an individual'svisual acuity.

BRIEF SUMMARY OF THE INVENTION

The present invention provides methods, devices, and systems forpredicting an optical acuity measure of an optical system of an eye. Anoptical acuity measure can be predicted by determining a point spreadfunction based on a wavefront measurement of an eye, convolving aresolution target with the point spread function to produce an image,and predicting the optical acuity measure of the optical system of theeye based on the image.

In a first aspect, the present invention provides a method forpredicting an optical acuity measure of an optical system of an eye. Themethod can include determining a vision characteristic-modified pointspread function based on a wavefront measurement of an eye; convolving aresolution target with the point spread function to produce an image;and predicting the optical acuity measure of the optical system of theeye based on the image. The resolution target can be selected from thegroup consisting of a single Snellen letter, a collection of Snellenletters, a plaid-type pattern, a resolution spoke, and an Archimedesspiral. The contrast of the resolution target can range from about 1% toabout 100%. The contrast of the resolution target can range from about10% to about 100%. The resolution target can be a resolution spokehaving an angular spacing that ranges from about 5° to about 30°. Theresolution target can be a resolution spoke having an angular spacing ofabout 15°. The resolution target can have a 512 pixel resolution.Relatedly, the resolution target can be a resolution spoke having anangular spacing greater than about 30°, and having a 1024 pixelresolution. The resolution target can also be a resolution spoke havingan angular spacing of about 60, and having a 2048 pixel resolution. Whatis more, an optical resolution measure of the eye can be based on theimage, and the optical acuity measure of the eye can be based on theoptical resolution measure. The optical resolution measure of the eyecan be based on Rayleigh's criterion as applied to the image. Theoptical resolution measure can be based on a sinusoidal interpretationof the addition of two Airy disks. Relatedly, discernability in theoptical resolution measure can be based on a contrast ratio of thesinusoidal interpretation. The optical acuity measure can be representedin Snellen format. The optical resolution measure can be represented inlogMAR format. The resolution target can be a resolution spoke, and theoptical acuity measure can be calculated from a resolution ringcalibration based on a 0.5 mm pupil diameter. The resolution target canbe a resolution spoke, and the optical acuity measure can be calculatedfrom a resolution ring calibration based on a defocused resolutionspoke. The resolution target can be a resolution spoke, and the opticalacuity measure can be based on a resolution ring calibration based onaberration-free cases of different pupil sizes ranging from about 0.25μm to about 2 mm. The optical system of the eye can comprise a corneaand a lens of the eye. The point spread function can incorporate aparameter based on a planned ablative surgical procedure. The resolutiontarget can be represented by a model. The image can be represented by amodel.

In another aspect, the present invention provides a method forpredicting an optical acuity measure of an optical system of an eye. Themethod can include determining a point spread function based on awavefront measurement of an eye; centering the point spread functionwith respect to the center of the resolution target; convolving aresolution target with the point spread function to produce an image;and predicting the optical acuity measure of the optical system of theeye based on the image. The point spread function can be centered basedon compensation for an averaged wavefront tilt. The point spreadfunction can be centered based on the formulas

$\frac{\partial{W\left( {r,\theta} \right)}}{\partial x} = {{\frac{\partial\;}{\partial x}{\sum\limits_{i = 1}^{N}\; {c_{i}{Z_{i}\left( {r,\theta} \right)}}}} = {\sum\limits_{i = 1}^{N}\; {c_{i}\frac{\partial{Z_{i}\left( {r,\theta} \right)}}{\partial x}}}}$$\frac{\partial{W\left( {r,\theta} \right)}}{\partial y} = {{\frac{\partial\;}{\partial y}{\sum\limits_{i = 1}^{N}\; {c_{i}{Z_{i}\left( {r,\theta} \right)}}}} = {\sum\limits_{i = 1}^{N}\; {c_{i}{\frac{\partial{Z_{i}\left( {r,\theta} \right)}}{\partial y}.}}}}$

The point spread function can be centered based on implementation of awavefront derivative as the average wavefront pixel difference betweentwo neighboring pixels in either the x- or y-direction. The point spreadfunction is centered based on the following formulas

${\frac{\partial{W\left( {r,\theta} \right)}}{\partial x} = {\frac{1}{n}{\sum\limits_{i}\; {\sum\limits_{j}\; \left( {W_{i,{j + 1}} - W_{i,j}} \right)}}}},\left( {r \leq 1} \right)$${\frac{\partial{W\left( {r,\theta} \right)}}{\partial y} = {\frac{1}{n}{\sum\limits_{i}\; {\sum\limits_{j}\; \left( {W_{{i + 1},j} - W_{i,j}} \right)}}}},{\left( {r \leq 1} \right).}$

The point spread function can be centered based on a calculated centerof gravity of the point spread function. The point spread function canbe centered based on the following formulas

$a_{x} = {\frac{\int{\int{{{xi}\left( {x,y} \right)}{x}{y}}}}{\int{\int\; {{i\left( {x,y} \right)}{x}{y}}}} = \frac{\sum\limits_{i}\; {\sum\limits_{j}\; {jI}_{i,j}}}{\sum\limits_{i}\; {\sum\limits_{l}\; I_{i,j}}}}$$a_{v} = {\frac{\int{\int{{{yi}\left( {x,y} \right)}{x}{y}}}}{\int{\int\; {{i\left( {x,y} \right)}{x}{y}}}} = {\frac{\sum\limits_{i}\; {\sum\limits_{j}\; {iI}_{i,j}}}{\sum\limits_{i}\; {\sum\limits_{l}\; I_{i,j}}}.}}$

The point spread function can be centered based on cross correlationbetween an input spoke and an output spoke. The point spread functioncan be centered based on the following formula

c(a _(x) ,a _(y))=l(x,y)⊕i(x−a _(x) ,y−a _(y)).

In another embodiment, the present invention provides a method fordetermining an optical acuity measure of an optical system of an eye.The method can include determining a vision characteristic-modifiedpoint spread function based on a wavefront measurement of an eye;convolving a resolution target with the point spread function to producean image; and determining the optical acuity measure of the opticalsystem of the eye based on the image.

In yet another embodiment, the present invention provides a method fordetermining an optical acuity measure of an optical system of an eye.The method can include determining a point spread function based on awavefront measurement of an eye; centering the point spread functionwith respect to the center of the resolution target; convolving aresolution target with the point spread function to produce an image;and determining the optical acuity measure of the optical system of theeye based on the image. The optical acuity measure can be determined bypredicting the measure.

In still another embodiment, the present invention provides a method forplanning an optical procedure for an eye based on a predicted opticalacuity measure of the eye. The method can include determining a putativeoptical procedure for an eye; determining avision-characteristic-modified point spread function based on awavefront measurement of an eye and the putative optical procedure forthe eye; and adjusting the putative optical procedure for the eye, suchthat a resolution target convolved with the point spread functionproduces an image that corresponds to an optimal optical acuity measureof the eye.

In another embodiment, the present invention provides a method fordetermining an estimated visual acuity of the eye. The method caninclude measuring visual distortion induced by optical aberrations of aneye of a patient to determine an imaging performance of the eye;constructing an acuity measurement model by simulating imagingperformance of the eye for a resolution target; and determining anestimated visual acuity of the eye using the acuity measurement model.The estimated visual acuity of the eye can be determined such that theestimated acuity accurately correlates to an actual acuity of the eye.

In yet another embodiment, the present invention provides a system forpredicting an optical acuity measure of an eye. The system can include amodule that determines a vision-characteristic-modified point spreadfunction based on a wavefront measurement of an eye; a module thatconvolves a resolution target with the point spread function to producean image; and a module that predicts the optical acuity measure of theeye based on the image. The system can also include an input thataccepts the wavefront measurement of the eye, and a module thatdetermines the wavefront measurement of the eye.

In another embodiment, the present invention provides a system fordetermining an estimated optical acuity of an eye. The system caninclude a module that measures visual distortion induced by opticalaberrations of an eye of an individual to determine an imagingperformance of the eye; a module that constructs an acuity measurementmodel by simulating imaging performance of the eye for a resolutiontarget; and a module that determines an estimated visual acuity of theeye using the acuity measurement model. The module that determines anestimated visual acuity can operate such that the estimated acuityaccurately correlates to an actual visual acuity of the eye. The presentinvention also provides a kit that includes a system for predicting anoptical acuity measure of an eye. The kit can also include instructionsto use the system in predicting an optical acuity measure of an eye.

In yet another embodiment, the present invention provides a system fordetermining an optical acuity measure of an eye. The system can includea module that determines a vision-characteristic-modified point spreadfunction based on a wavefront measurement of an eye; a module thatconvolves a resolution target with the point spread function to producean image; and a module that determines the optical acuity measure of theeye based on the image.

In another embodiment, the present invention provides a system fordetermining an optical acuity measure of an eye. The system can includea module that determines a point spread function based on a wavefrontmeasurement of an eye; a module that centers the point spread functionwith respect to the center of the resolution target; a module thatconvolves a resolution target with the point spread function to producean image; and a module that determines the optical acuity measure of theeye based on the image.

In still another embodiment, the present invention provides a system forpredicting an optical acuity measure of an eye. The system can includesa module that determines a point spread function based on a wavefrontmeasurement of an eye; a module that centers the point spread functionwith respect to the center of the resolution target; a module thatconvolves a resolution target with the point spread function to producean image; and a module that predicts the optical acuity measure of theeye based on the image.

For a fuller understanding of the nature and advantages of the presentinvention, reference should be had to the ensuing detailed descriptiontaken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a laser ablation system according to an embodiment ofthe present invention.

FIG. 2 illustrates a simplified computer system according to anembodiment of the present invention.

FIG. 3 illustrates a wavefront measurement system according to anembodiment of the present invention.

FIG. 3A illustrates another wavefront measurement system according to anembodiment of the present invention.

FIG. 4A shows a resolution target that includes the eye chart letter Ecorresponding to a visual acuity measure of 20/20.

FIG. 4B shows a resolution target of the eye chart letter Ecorresponding to a visual acuity measure of 20/40.

FIG. 4C shows a resolution target of the eye chart letter Ecorresponding to a visual acuity measure of 20/80.

FIG. 4D shows a resolution target of an eye chart that includes the eyechart letter E corresponding to visual acuity measures of 20/20, 20/40,20/60, and 20/80.

FIG. 5A illustrates a plaid-type resolution target at high resolutioncontrast.

FIG. 5B illustrates a plaid-type resolution target at low resolutioncontrast.

FIG. 6A depicts a resolution spoke type of resolution target at highresolution contrast.

FIG. 6B depicts a resolution spoke type of resolution target at lowresolution contrast.

FIG. 6C depicts an Archimedes spiral type of resolution target at highresolution contrast.

FIG. 6D depicts an Archimedes spiral type of resolution target at lowresolution contrast.

FIG. 7 shows a profile of two Airy disks.

FIG. 8A illustrates a contrast adjusted sine wave.

FIG. 8B illustrates two bars of a convolved resolution target of theplaid type.

FIG. 8C illustrates two rays of a convolved resolution spoke.

FIG. 9A shows a contrast reversal resolution spoke with 0.25D focusingerror for a 6 mm pupil with angular spacing of 6°.

FIG. 9B shows a contrast reversal resolution spoke with 0.25D focusingerror for a 6 mm pupil with angular spacing of 10°.

FIG. 9C shows an optical transfer function for the blurred resolutionspoke shown in FIG. 6B.

FIG. 10A illustrates a resolution spoke having a resolution ringcorresponding to an optical acuity of 20/10.

FIG. 10B illustrates a resolution spoke having a resolution ringcorresponding to an optical acuity of 20/20.

FIG. 10C illustrates a resolution spoke having a resolution ringcorresponding to an optical acuity of 20/40.

FIG. 10D illustrates a resolution spoke having a resolution ringcorresponding to an optical acuity of 20/80.

FIG. 10E illustrates a resolution spoke having a resolution ringcorresponding to an optical acuity of 20/160.

FIG. 11A depicts a convolved resolution spoke without re-centration.

FIG. 11B depicts a convolved resolution spoke with re-centration.

FIG. 12 illustrates the correlation of the measured UCLM (uncorrectedvisual acuity with logMAR) versus the predicted UCLM for 11 LASIK eyes 1year post surgery.

FIG. 13 shows a convolved Archimedes spiral resolution target.

FIG. 14 depicts a convolved Archimedes spiral resolution target.

FIG. 15A shows a procedural flowchart.

FIG. 15B shows a system diagram.

FIG. 15C shows a system diagram.

FIG. 15D shows a system diagram.

FIG. 15E shows a system diagram.

FIG. 16 depicts a schematic representation of tangential acuity.

FIG. 17 illustrates a schematic representation of radial acuity.

FIG. 18 illustrates a segment of a convolved Archimedes spiral.

FIG. 19 shows a convolved resolution spoke.

DETAILED DESCRIPTION OF THE INVENTION

Turning now to the drawings, FIG. 1 illustrates a laser eye surgerysystem 10 of the present invention, including a laser 12 that produces alaser beam 14. Laser 12 is optically coupled to laser delivery optics16, which directs laser beam 14 to an eye E of patient P. A deliveryoptics support structure (not shown here for clarity) extends from aframe 18 supporting laser 12. A microscope 20 is mounted on the deliveryoptics support structure, the microscope often being used to image acornea of eye E.

Laser 12 generally comprises an excimer laser, ideally comprising anargon-fluorine laser producing pulses of laser light having a wavelengthof approximately 193 nm. Laser 12 will preferably be designed to providea feedback stabilized fluence at the patient's eye, delivered viadelivery optics 16. The present invention may also be useful withalternative sources of ultraviolet or infrared radiation, particularlythose adapted to controllably ablate the corneal tissue without causingsignificant damage to adjacent and/or underlying tissues of the eye.Such sources include, but are not limited to, solid state lasers andother devices which can generate energy in the ultraviolet wavelengthbetween about 185 and 205 nm and/or those which utilizefrequency-multiplying techniques. Hence, although an excimer laser isthe illustrative source of an ablating beam, other lasers may be used inthe present invention.

Laser system 10 will generally include a computer or programmableprocessor 22. Processor 22 may comprise (or interface with) aconventional PC system including the standard user interface devicessuch as a keyboard, a display monitor, and the like. Processor 22 willtypically include an input device such as a magnetic or optical diskdrive, an internet connection, or the like. Such input devices willoften be used to download a computer executable code from a tangiblestorage media 29 embodying any of the methods of the present invention.Tangible storage media 29 may take the form of a floppy disk, an opticaldisk, a data tape, a volatile or non-volatile memory. RAM, or the like,and the processor 22 will include the memory boards And other standardcomponents of modern computer systems for storing and executing thiscode. Tangible storage media 29 may optionally embody wavefront sensordata, wavefront gradients, a wavefront elevation map, a treatment map, acorneal elevation map, and/or an ablation table. While tangible storagemedia 29 will often be used directly in cooperation with a input deviceof processor 22, the storage media may also be remotely operativelycoupled with processor by means of network connections such as theInternet, and by wireless methods such as infrared, Bluetooth, or thelike.

Laser 12 and delivery optics 16 will generally direct laser beam 14 tothe eye of patient P under the direction of a computer 22. Computer 22will often selectively adjust laser beam 14 to expose portions of thecornea to the pulses of laser energy so as to effect a predeterminedsculpting of the cornea and alter the refractive characteristics of theeye. In many embodiments, both laser beam 14 and the laser deliveryoptical system 16 will be under computer control of processor 22 toeffect the desired laser sculpting process, with the processor effecting(and optionally modifying) the pattern of laser pulses. The pattern ofpulses may by summarized in machine readable data of tangible storagemedia 29 in the form of a treatment table, and the treatment table maybe adjusted according to feedback input into processor 22 from anautomated image analysis system in response to feedback data providedfrom an ablation monitoring system feedback system. Optionally, thefeedback may be manually entered into the processor by a systemoperator. Such feedback might be provided by integrating the wavefrontmeasurement system described below with the laser treatment system 10,and processor 22 may continue and/or terminate a sculpting treatment inresponse to the feedback, and may optionally also modify the plannedsculpting based at least in part on the feedback. Measurement systemsare further described in U.S. Pat. No. 6,315,413, the full disclosure ofwhich is incorporated herein by reference.

Laser beam 14 may be adjusted to produce the desired sculpting using avariety of alternative mechanisms. The laser beam 14 may be selectivelylimited using one or more variable apertures. An exemplary variableaperture system having a variable iris and a variable width slit isdescribed in U.S. Pat. No. 5,713,892, the full disclosure of which isincorporated herein by reference. The laser beam may also be tailored byvarying the size and offset of the laser spot from an axis of the eye,as described in U.S. Pat. Nos. 5,683,379, 6.203,539, and 6,331,177, thefull disclosures of which are incorporated herein by reference.

Still further alternatives are possible, including scanning of the laserbeam over the surface of the eye and controlling the number of pulsesand/or dwell time at each location, as described, for example, by U.S.Pat. No. 4,665,913, the full disclosure of which is incorporated hereinby reference; using masks in the optical path of laser beam 14 whichablate to vary the profile of the beam incident on the cornea, asdescribed in U.S. Pat. No. 5,807,379, the full disclosure of which isincorporated herein by reference; hybrid profile-scanning systems inwhich a variable size beam (typically controlled by a variable widthslit and/or variable diameter iris diaphragm) is scanned across thecornea; or the like. The computer programs and control methodology forthese laser pattern tailoring techniques are well described in thepatent literature.

Additional components and subsystems may be included with laser system10, as should be understood by those of skill in the art. For example,spatial and/or temporal integrators may be included to control thedistribution of energy within the laser beam, as described in U.S. Pat.No. 5,646,791, the full disclosure of which is incorporated herein byreference. Ablation effluent evacuators/filters, aspirators, and otherancillary components of the laser surgery system are known in the art.Further details of suitable systems for performing a laser ablationprocedure can be found in commonly assigned U.S. Pat. Nos. 4,665,913,4,669,466, 4,732,148, 4,770,172, 4,773,414, 5,207,668, 5,108,388,5,219,343, 5,646,791 and 5,163,934, the complete disclosures of whichare incorporated herein by reference. Suitable systems also includecommercially available refractive laser systems such as thosemanufactured and/or sold by Alcon, Bausch & Lomb, Nidek, WaveLight,LaserSight, Schwind, Zeiss-Meditec, and the like. Basis data can befurther characterized for particular lasers or operating conditions, bytaking into account localized environmental variables such astemperature, humidity, airflow, and aspiration.

FIG. 2 is a simplified block diagram of an exemplary computer system 22that may be used by the laser surgical system 10 of the presentinvention. Computer system 22 typically includes at least one processor52 which may communicate with a number of peripheral devices via a bussubsystem 54. These peripheral devices may include a storage subsystem56, comprising a memory subsystem 58 and a file storage subsystem 60,user interface input devices 62, user interface output devices 64, and anetwork interface subsystem 66. Network interface subsystem 66 providesan interface to outside networks 68 and/or other devices, such as thewavefront measurement system 30.

User interface input devices 62 may include a keyboard, pointing devicessuch as a mouse, trackball, touch pad, or graphics tablet, a scanner,foot pedals, a joystick, a touchscreen incorporated into the display,audio input devices such as voice recognition systems, microphones, andother types of input devices. User input devices 62 will often be usedto download a computer executable code from a tangible storage media 29embodying any of the methods of the present invention. In general, useof the term “input device” is intended to include a variety ofconventional and proprietary devices and ways to input information intocomputer system 22.

User interface output devices 64 may include a display subsystem, aprinter, a fax machine, or non-visual displays such as audio outputdevices. The display subsystem may be a cathode ray tube (CRT), aflat-panel device such as a liquid crystal display (LCD), a projectiondevice, or the like. The display subsystem may also provide a non-visualdisplay such as via audio output devices. In general, use of the term“output device” is intended to include a variety of conventional andproprietary devices and ways to output information from computer system22 to a user.

Storage subsystem 56 can store the basic programming and data constructsthat provide the functionality of the various embodiments of the presentinvention. For example, a database and modules implementing thefunctionality of the methods of the present invention, as describedherein, may be stored in storage subsystem 56. These software modulesare generally executed by processor 52. In a distributed environment,the software modules may be stored on a plurality of computer systemsand executed by processors of the plurality of computer systems. Storagesubsystem 56 typically comprises memory subsystem 58 and file storagesubsystem 60.

Memory subsystem 58 typically includes a number of memories including amain random access memory (RAM) 70 for storage of instructions and dataduring program execution and a read only memory (ROM) 72 in which fixedinstructions are stored. File storage subsystem 60 provides persistent(non-volatile) storage for program and data files, and may includetangible storage media 29 (FIG. 1) which may optionally embody wavefrontsensor data, wavefront gradients, a wavefront elevation map, a treatmentmap, and/or an ablation table. File storage subsystem 60 may include ahard disk drive, a floppy disk drive along with associated removablemedia, a Compact Digital Read Only Memory (CD-ROM) drive, an opticaldrive, DVD, CD-R, CD-RW, solid-state removable memory, and/or otherremovable media cartridges or disks. One or more of the drives may belocated at remote locations on other connected computers at other sitescoupled to computer system 22. The modules implementing thefunctionality of the present invention may be stored by file storagesubsystem 60.

Bus subsystem 54 provides a mechanism for letting the various componentsand subsystems of computer system 22 communicate with each other asintended. The various subsystems and components of computer system 22need not be at the same physical location but may be distributed atvarious locations within a distributed network. Although bus subsystem54 is shown schematically as a single bus, alternate embodiments of thebus subsystem may utilize multiple busses.

Computer system 22 itself can be of varying types including a personalcomputer, a portable computer, a workstation, a computer terminal, anetwork computer, a control system in a wavefront measurement system orlaser surgical system, a mainframe, or any other data processing system.Due to the ever-changing nature of computers and networks, thedescription of computer system 22 depicted in FIG. 2 is intended only asa specific example for purposes of illustrating one embodiment of thepresent invention. Many other configurations of computer system 22 arepossible having more or less components than the computer systemdepicted in FIG. 2.

Referring now to FIG. 3, one embodiment of a wavefront measurementsystem 30 is schematically illustrated in simplified form. In verygeneral terms, wavefront measurement system 30 is configured to senselocal slopes of a gradient map exiting the patient's eye. Devices basedon the Hartmann-Shack principle generally include a lenslet array tosample the gradient map uniformly over an aperture, which is typicallythe exit pupil of the eye. Thereafter, the local slopes of the gradientmap are analyzed so as to reconstruct the wavefront surface or map.

More specifically, one wavefront measurement system 30 includes an imagesource 32, such as a laser, which projects a source image throughoptical tissues 34 of eye E so as to form an image 44 upon a surface ofretina R. The image from retina R is transmitted by the optical systemof the eye (e.g., optical tissues 34) and imaged onto a wavefront sensor36 by system optics 37. The wavefront sensor 36 communicates signals toa computer system 22′ for measurement of the optical errors in theoptical tissues 34 and/or determination of an optical tissue ablationtreatment program. Computer 22′ may include the same or similar hardwareas the computer system 22 illustrated in FIGS. 1 and 2. Computer system22′ may be in communication with computer system 22 that directs thelaser surgery system 10, or some or all of the components of computersystem 22, 22′ of the wavefront measurement system 30 and laser surgerysystem 10 may be combined or separate. If desired, data from wavefrontsensor 36 may be transmitted to a laser computer system 22 via tangiblemedia 29, via an I/O port, via an networking connection 66 such as anintranet or the Internet, or the like.

Wavefront sensor 36 generally comprises a lenslet array 38 and an imagesensor 40. As the image from retina R is transmitted through opticaltissues 34 and imaged onto a surface of image sensor 40 and an image ofthe eye pupil P is similarly imaged onto a surface of lenslet array 38,the lenslet array separates the transmitted image into an array ofbeamlets 42, and (in combination with other optical components of thesystem) images the separated beamlets on the surface of sensor 40.Sensor 40 typically comprises a charged couple device or “CCD,” andsenses the characteristics of these individual beamlets, which can beused to determine the characteristics of an associated region of opticaltissues 34. In particular, where image 44 comprises a point or smallspot of light, a location of the transmitted spot as imaged by a beamletcan directly indicate a local gradient of the associated region ofoptical tissue.

Eye E generally defines an anterior orientation ANT and a posteriororientation POS. Image source 32 generally projects an image in aposterior orientation through optical tissues 34 onto retina R asindicated in FIG. 3. Optical tissues 34 again transmit image 44 from theretina anteriorly toward wavefront sensor 36. Image 44 actually formedon retina R may be distorted by any imperfections in the eye's opticalsystem when the image source is originally transmitted by opticaltissues 34. Optionally, image source projection optics 46 may beconfigured or adapted to decrease any distortion of image 44.

In some embodiments, image source optics 46 may decrease lower orderoptical errors by compensating for spherical and/or cylindrical errorsof optical tissues 34. Higher order optical errors of the opticaltissues may also be compensated through the use of an adaptive opticelement, such as a deformable mirror (described below). Use of an imagesource 32 selected to define a point or small spot at image 44 uponretina R may facilitate the analysis of the data provided by wavefrontsensor 36. Distortion of image 44 may be limited by transmitting asource image through a central region 48 of optical tissues 34 which issmaller than a pupil 50, as the central portion of the pupil may be lessprone to optical errors than the peripheral portion. Regardless of theparticular image source structure, it will be generally be beneficial tohave a well-defined and accurately formed image 44 on retina R.

In one embodiment, the wavefront data may be stored in a computerreadable medium 29 or a memory of the wavefront sensor system 30 in twoseparate arrays containing the x and y wavefront gradient valuesobtained from image spot analysis of the Hartmann-Shack sensor images,plus the x and y pupil center offsets from the nominal center of theHartmann-Shack lenslet array, as measured by the pupil camera 51 (FIG.3) image. Such information contains all the available information on thewavefront error of the eye and is sufficient to reconstruct thewavefront or any portion of it. In such embodiments, there is no need toreprocess the Hartmann-Shack image more than once, and the data spacerequired to store the gradient array is not large. For example, toaccommodate an image of a pupil with an 8 mm diameter, an array of a20×20 size (i.e., 400 elements) is often sufficient. As can beappreciated, in other embodiments, the wavefront data may be stored in amemory of the wavefront sensor system in a single array or multiplearrays.

While the methods of the present invention will generally be describedwith reference to sensing of an image 44, a series of wavefront sensordata readings may be taken. For example, a time series of wavefront datareadings may help to provide a more accurate overall determination ofthe ocular tissue aberrations. As the ocular tissues can vary in shapeover a brief period of time, a plurality of temporally separatedwavefront sensor measurements can avoid relying on a single snapshot ofthe optical characteristics as the basis for a refractive correctingprocedure. Still further alternatives are also available, includingtaking wavefront sensor data of the eye with the eye in differingconfigurations, positions, and/or orientations. For example, a patientwill often help maintain alignment of the eye with wavefront measurementsystem 30 by focusing on a fixation target, as described in U.S. Pat.No. 6,004,313, the full disclosure of which is incorporated herein byreference. By varying a position of the fixation target as described inthat reference, optical characteristics of the eye may be determinedwhile the eye accommodates or adapts to image a field of view at avarying distance and/or angles.

The location of the optical axis of the eye may be verified by referenceto the data provided from a pupil camera 52. In the exemplaryembodiment, a pupil camera 52 images pupil 50 so as to determine aposition of the pupil for registration of the wavefront sensor datarelative to the optical tissues.

An alternative embodiment of a wavefront measurement system isillustrated in FIG. 3A. The major components of the system of FIG. 3Aare similar to those of FIG. 3. Additionally, FIG. 3A includes anadaptive optical element 53 in the form of a deformable mirror. Thesource image is reflected from deformable mirror 98 during transmissionto retina R, and the deformable mirror is also along the optical pathused to form the transmitted image between retina R and imaging sensor40. Deformable mirror 98 can be controllably deformed by computer system22 to limit distortion of the image formed on the retina or ofsubsequent images formed of the images formed on the retina, and mayenhance the accuracy of the resultant wavefront data. The structure anduse of the system of FIG. 3A are more fully described in U.S. Pat. No.6,095,651, the full disclosure of which is incorporated herein byreference.

The components of an embodiment of a wavefront measurement system formeasuring the eye and ablations may comprise elements of a VISXWaveScan®, available from VISX, INCORPORATED of Santa Clara, Calif. Oneembodiment includes a WaveScan® with a deformable mirror as describedabove. An alternate embodiment of a wavefront measuring system isdescribed in U.S. Pat. No. 6,271,915, the full disclosure of which isincorporated herein by reference. It is appreciated that any wavefrontaberrometer could be employed for use with the present invention.

The present invention is useful for enhancing the accuracy and efficacyof photorefractive keratectomy (PRK), laser in situ keratomileusis(LASIK), laser assisted epithelium keratomileusis (LASEK), and the like.The present invention can provide enhanced optical correction approachesby improving the methodology for scaling an optical shape, or bygenerating or deriving new optical shapes, and the like.

The techniques of the present invention can be readily adapted for usewith existing laser systems, including the VISX Excimer laser eyesurgery systems commercially available from VISX of Santa Clara, Calif.Other suitable laser systems are manufactured by Alcon, Bausch & Lomb,Wavelight, Schwind, Zeiss-Meditec, Lasersight, Nidek and the like.

Standard point spread functions may sometimes be beneficial fordetermining visual acuity, but may not provide desirable results in somecircumstances. It can be advantageous to specialize a point spreadfunction to a particular optical system. For example, a particularoptical system such as an eye may include factors such as chromaticaberrations, retinal sensitivity, or Stiles-Crawford effects that canaffect vision characteristics, and it may be desirable to modify a pointspread function based on these types of factors. Described herein are anumber of approaches to modify a standard point spread function toarrive at a such a vision characteristic-modified point spread function.

The present invention allows predicting a measure of objective opticalacuity that is based on the optical characteristics of the cornea andlens of a patient's eye. Specifically, the present invention providessystems, methods, and devices for determining the optical quality of anindividual's eye, based on wavefront measurements. With the advent ofwavefront technology, it has become possible to objectively and moreaccurately determine optical aberrations in the entire eye, includingthe cornea and the crystalline lens. Objective visual acuity, or opticalacuity, can be predicted based on the wavefront measurements of humaneyes.

The present invention can use a visual distortion measurement induced byoptical aberrations of an individual's eye to determine an imagingperformance of the eye. Often, the visual distortion measurement can bea vision characteristic-modified visual distortion measurement. Anacuity measurement model can then be constructed by simulating theimaging performance of the eye for a resolution target. It is thenpossible to determine an estimated visual or optical acuity of the eyeusing the acuity measurement model. The visual acuity model can beestimated such that the estimated acuity accurately correlates to anactual visual or optical acuity of the eye. The imaging performance ofthe eye can be characterized in various ways, including point spreadfunction and ray tracing approaches.

For example, the present invention will often involve determining apoint spread function based on a wavefront measurement of an eye,convolving a resolution target with the point spread function to producean image; and determining the measure of objective optical acuity of theeye based on the image.

Determining a Point Spread Function Based on a Wavefront Measurement ofan Eye

In wavefront analysis, a highly collimated beam of light is projected onthe retina, and the reflected outgoing beam is processed to create awavefront aberration map. The aberration map represents aberrationsintroduced to the waveform as it passes through the optical system ofthe eye.

There are many known methods of processing the reflected outgoing beamto create the map. For example, in the Hartmann-Shack method, a singlelaser beam is projected as a spot on the retina. The reflected beam iscaptured by an array of small lenslets, which focus these rays into anarray of spots on a cathode-coupling device (CCD) camera or other imagecapture device. The resulting spots are used to create the wavefrontmap. Wavefront measurement devices are commercially available, includingthe WaveScan® system available from VISX. Incorporated.

A useful feature of the wavefront aberration map is the point spreadfunction (PSF), which can represent the visual distortion that aparticular patient experiences with their current optical aberrations.In this way, the PSF can be used to predict or otherwise characterizethe performance of an optical system. Generally, the PSF is based on theintensity distribution of an ideal point-like source in the focal planeresulting from the diffraction by the optics of the system. The PSF canbe a three-dimensional graphic, or mathematical representation of theimage of a point source produced by a lens or optical system.

With wavefront technologies, it is possible to calculate the pointspread function (PSF) based on the optical path difference (OPD) of theoptical system of the eve, where the optical system of the eye caninclude the cornea and lens. The optical path difference can be based ondeviations in an incoming wave as compared to an ideal spherical ingoingwave. There are standard software packages available that take sensordata from wavefront devices and calculate the optical path differenceand point spread function of the optical system.

Calculation of Point Spread Function

The point spread function (PSF) will typically be calculated based onthe wavefront data. For example, a wavefront with aberrations can bedenoted by W(r, θ). It is also possible to consider effects such as thepolychromatic effect, the human eye's chromatic aberrations, theStiles-Crawford effect, as well as the retinal spectral responsefunction, when determining a point spread function, and in particular avision characteristic-modified point spread function. Accordingly, manyof the implementations of the point spread function described herein maynot refer to a standard point spread function, but rather to a visioncharacteristic-modified point spread function. Considering theseeffects, for example, the polychromatic PSF can be expressed as

${{P\; S\; F} = {\sum\limits_{\lambda}\; {{R(\lambda)}{{F\; F\; {T\left( {{P_{SC}(r)}{\exp \left\lbrack {{- j}{\frac{2\pi}{\lambda}\left\lbrack {{W\left( {r,\theta} \right)} + {{aD}(\lambda)}} \right\rbrack}} \right\rbrack}} \right)}}}^{2}}}},$

where R(λ) is the retina spectral response function and can beapproximated to

R(λ)=e ^(−300(λ−λ) ⁰ ⁾ ²

and P_(sc)(r) is the pupil apodization function (Stiles-Crawford effect)and can be written as

${P_{sc}(r)} = 10^{{- \rho}\frac{r^{2}}{R^{2}}}$

and D(λ) is chromatic aberration at wavelength λ and can be close to

D(λ)=−21.587+92.872−134.98λ²+67.4072λ³

and the central wavelength λ₀ can be taken as 0.55 μm (as all wavelengthunits in the above formulae can be in μm). The pupil apodizationstrength parameter ρ can be taken as 0.06. α can represent theconversion factor from diopter to optical path difference (OPD). FFT candenote a fast Fourier transform and |*| denotes the module of a complexnumber.

In implementing the polychromatic wavelengths, it has been found that 7wavelengths at 0.40, 0.45, 0.50, 0.55, 0.60, 0.65, and 0.70 μm,respectively, give adequate approximation for the entire white-lightspectra.

Convolving a Resolution Target with the Point Spread Function to Producean Image

Once a point spread function or other visual distortion measurement hasbeen determined based on a wavefront measurement of an eye, it ispossible to simulate performance of the optical system, typically byconvolving an object such as a resolution target with the PSF or othermeasurement to produce an acuity measurement model, often in the form ofa blurred image. This is because the PSF is considered to be a goodmeasure of the errors and artifacts that appear in an image produced byan optical system.

Construction of Resolution Targets

As noted above, resolution targets can be convolved with the pointspread function as calculated from the wavefront measurements. It isuseful to construct a resolution target in a way that determination ofresolution or optical quality can be deduced from the blurred image ofthe target. A resolution target can include resolution lines or segmentsthat are representative of a broad spectrum of spatial frequencies. Itmay also be desirable that a resolution target be capable ofrepresenting different contrast sensitivities. Often, resolution targetswill be represented by mathematical or computer models, or otherwiseconstructed with software modules, hardware modules, or modulescontaining both software and hardware components.

A first resolution target technique is based on single eye chartletters, such as Snellen F, having different, sizes. The size of theletter can be determined based on the size of the expecteddiffraction-limited point spread function (PSF). For instance, eachhorizontal stroke in a 20/20 letter E has an angular resolutioncorresponding to one arc minute. Thus, if the diffraction limited PSF ishalf an arc minute spanning four pixels, then each horizontal stroke inthe letter E spans a width of eight pixels. Similarly, the height ofeach horizontal stroke, as well as the space between each horizontalstroke, is eight pixels. Thus, the height of the letter E spans 40pixels (8*5). As the letter E is square, it also spans 40 pixels inwidth.

FIGS. 4A, 4B, and 4C show resolution targets that include the eye chartletter E corresponding to a visual acuity measure of 20/20, 20/40, and20/80, respectively. Resolution targets such as these can be used in theprediction or evaluation of objective optical acuity. Determination ofan objective optical acuity with this approach typically involvesmultiple tests with resolution targets at varying sizes. Typically,larger letters that have been convolved with a point spread function arediscernable. However, as the size of the letter decreases, the blurringeffect of convolution can become more significant. In determiningoptical acuity, this approach can involve determining the resolutiontarget size at which the blurred image is barely discernable.

A second resolution target technique involves the use of an entire eyechart as the resolution target, as shown in FIG. 4D, which includes theeye chart letter E corresponding to visual acuity measures of 20/20,20/40, 20/60, and 20/80. The entire eye chart can be convolved with thepoint spread function (PSF), and resolution can be estimated byevaluating the contrast loss in different size letters.

A third resolution target technique involves the use of a plaid-typepattern resolution chart. Such a resolution target can be at highcontrast, as shown in FIG. 5A (100% contrast), and at low contrast, asshown in FIG. 5 (10% contrast).

The finest lines with the highest spatial resolution or frequency (forexample, one pixel width), are usually disposed in the middle of thechart. Traveling outward from the middle, the resolution lines can beincrementally larger in size and spacing. For example, the nextresolution lines can correspond to one half the spatial resolution orfrequency of the immediate inner lines. If this progression is followed,as shown in FIGS. 5A and 5B, the outermost resolution lines can be 32times larger, or 32 pixels in width. Thus, for example, if the finestlines can represent 20/10 visual acuity, the thickest lines canrepresent 20/320 visual acuity.

Convolution of plaid-type charts with the point spread function providesa blurred image that can be used to determine the optical acuity of theeye. As compared to the eye letter chart, plaid charts may be devoid oforientation bias. For example, the letter E is more biased in horizontalorientation, as it has three horizontal strokes and one vertical stroke.The plaid type resolution target approach typically involves evaluatingseveral resolution lines in order to estimate the optical acuity. Also,as the lines are typically incremented in size, for example doubling insize going from the inside to the outside, the acuity measurementresults are correspondingly incremented. For example, with such charts,it may be possible to obtain acuity of 20/10, 20/20, 20/40, 20/80,20/160 and so on.

A fourth resolution target technique involves the use of a resolutionspoke constructed with continuous resolution from center (highestresolution) to periphery (lowest resolution). FIG. 6A illustrates aresolution spoke with 20° spacing and 100% contrast. The letter chartsdiscussed above contain uniform lines and typically correspond only todiscrete spatial frequencies, whereas a resolution spoke resolutiontarget can have lines corresponding to a range of spatial frequencies.In other words, the change in spatial resolution of the spoke lines issubstantially continuous, with higher resolution toward the center ofthe spoke, and lower resolution toward the outer periphery of the spoke.In some cases, the resolution may not be precisely continuous, however,as the resolution spoke target, the convolved image thereof, or both,may be pixelized. Once the resolution target is convolved with the pointspread function, it is possible to determine circles that correspond tooptical acuity measurements. Thus, the optical acuity can be determinedwith very fine stepping.

The angular spacing can be controlled according to the desiredresolution. For instance, when the spoke is to be used for veryaccurate, low aberration acuity testing, the angular spacing can be verysmall to construct very fine spokes. On the other hand, if the target isto use the resolution spoke to predict a large resolution range, thenthe angular spacing can be much larger. The resolution spokesillustrated here are constructed with different angular spacing andcontrast. In many of the examples provided herein, a 30° is used in thecalculations. In terms of resolution contrast, FIG. 6A depicts aresolution spoke type of resolution target at high resolution contrast(e.g. 100%), whereas FIG. 6B depicts a resolution spoke type ofresolution target at low resolution contrast (e.g. 10%).

It is possible that the resolution of the optical system can be changingin radial direction as well as in a tangential direction. As shown inFIG. 16, the tangential resolution or acuity can remain constant, as theradial resolution varies. Similarly, as shown in FIG. 17, the radialresolution or acuity can remain constant, as the tangential resolutionvaries. Relatedly, the vertical resolution may differ from horizontalresolution. A fifth resolution target technique involves the use of anArchimedes spiral, as shown in FIGS. 6C and 6D. With this approach,resolution in the radial direction can be evaluated, according to thedesired resolution, in comparison to the resolution spoke, which can beused to evaluate resolution in the tangential direction.

For instance, when the spiral is to be used for very accurate, lowaberration radial acuity testing, the spirals can be placed very closelyto one another, creating a densely arranged target with many spiralsfrom the inside to the outside. Relatedly, when the spiral is used forvery accurate, low aberration radial acuity testing, the spirals can bemake very thick. In terms of resolution contrast, FIG. 6C depicts anArchimedes spiral type of resolution target at high resolution contrast(e.g. 100%), whereas FIG. 6D depicts an Archimedes spiral type ofresolution target at low resolution contrast (e.g. 10%).

A sixth approach involves a combination of a resolution spoke approachand an Archimedes spiral approach to obtain a real resolution measure.This approach is similar to combining two vectors, and can berepresented by the following formula

r=√(r ₁ ² +r ₂ ²)

where r denotes a real resolution. r₁ denotes a resolution estimatebased on a resolution spoke approach, and r₂ denotes a resolutionestimate based on an Archimedes spiral approach.

The resolution targets can also account for the contrast variation undersimilar acuity testing conditions. For instance, a 10% contrast acuitycan be implemented by convolving a 10% contrast resolution target with apoint spread function (PSF). FIGS. 5B, 6B, and 6D show the resolutiontarget or resolution spoke at a low 10% contrast, whereas FIGS. 5A, 6Aand 6C represent a high 100% contrast. Contrast can be defined as thedifference in illumination between the maximum intensity and the minimumintensity, divided by the sum of the maximum intensity and the minimumintensity. Thus, contrast of the resolution target can be defined by thefollowing formula.

contrast=(i _(max) −i _(min))/(i _(max) +i _(min))

Determining the Measure of Objective Optical Acuity of the Eye Based onthe Image

As noted above, a resolution target or a resolution target model can beconvolved with a point spread function to produce a blurred image or ablurred image model. By evaluating the degree of blurring in the image,it is possible to determine the resolution of the optical system. Forexample, two resolution lines may be blurred to the extent that they areno longer discernable. On the other hand, the lines may be blurred yetstill be discernable from each other. In the case of a convolvedresolution spoke, there may be a certain resolution radius inside ofwhich the spokes are not discernable, but outside of which the spokesare still discernable. Mathematical approaches can be used to determinewhat is discernable and what is not. Such determinations ofdiscernability can be based on the analysis of intensity patterns of aresolution target, or models thereof, that have been convolved with apoint spread function.

For example, the prediction or evaluation of optical acuity can be basedon the analysis of the pixel values on a convolved dark area versus alight area. If the PSF is large enough, then it can convolve and blurthe resolution spoke to a degree to which inside a circle having acertain radius, it is not possible to distinguish or discern betweenblack and white areas. Yet outside of the circle, it is still possibleto distinguish or discern the black and white areas. Accordingly, theradius of this circle can define the resolution of the optical system ofthe eye. As discussed below, it is possible to use Rayleigh's criterionto determine the appropriate resolution ring for determining the opticalacuity of the optical system.

Resolution Determination

Determination of the optical resolution may be based on Rayleigh'scriterion. For a diffraction-limited optical system with a circularaperture, operating in the absence of aberrations, the PSF can berepresented by an Airy disk.

According to the Rayleigh criterion, when two diffraction-limited pointsources (Airy disks) are separated to a distance such that the firstdark ring of one spot lies directly beneath the peak of the other spot,then the two spots can be considered to be discernable. The profile ofthe two added Airy discs is shown in FIG. 7, where the y-axis representsthe normalized intensity, and the x-axis represents the spatialdistance. These two Airy disks are separated by 1.22π radians. Theprofile of the addition of these two Airy disks can be written as

${{i(r)} = {\left\lbrack \frac{2\; {J_{1}(r)}}{r} \right\rbrack^{2} + \left\lbrack \frac{2\; {J_{1}\left( {r + {1.22\; \pi}} \right)}}{r + {1.22\; \pi}} \right\rbrack^{2}}},$

where i(r) is the intensity as a function of radius. As shown in themiddle of the figure, the addition of the profiles results in two peaksand a valley therebetween. Solving this equation for the peak and valleygives a ratio of valley intensity to peak intensity of 0.7346 to 1. Thiscontrast ratio represents the intensity contrast between the peak andthe valley. According to this approach, if the contrast ratio of aresolution ring on a convolved resolution spoke is less than 0.7346, theresolution ring at that distance is considered to be discernable. Inthis way, the resolution determination can be based on Rayleigh'scriterion. Results obtained from the Airy disk can form the basis forother approaches to determining discernability.

Instead of using the Airy disk approach to determine what isdiscernable, it is possible to use a convolved resolution spoke image. Acircle at a given radial distance from the center of a convolved spokecan produce a sinusoidal signal. When a contrast adjusted sinusoidalsignal has 1 and 0.7346 as maximum and minimum intensity values, asshown in FIG. 8A, the expected ratio of averaged left quadrant to rightquadrant can be expressed as

${\rho = {\frac{\int_{0}^{\pi/2}{\left\lbrack {a_{0} + {b_{0}{\cos \left( {\theta + {\pi/2}} \right)}}} \right\rbrack \ {\theta}}}{\int_{\pi/2}^{\pi}{\left\lbrack {a_{0} + {b_{0}{\cos \left( {\theta + {\pi/2}} \right)}}} \right\rbrack \ {\theta}}} = a_{0}}},$

where a₀=0.8673 (average intensity value at left quadrant—dark) andb₀=0.1327 (average intensity value at right quadrant—light).

According to this approach, when two resolution spokes or lines areseparated to a distance according to the Rayleigh's criterion, and ifthe contrast ratio of the darker portion (valley) to the brighterportion (peak) of the convolved spoke is smaller than 0.8673, then thetwo spokes or lines can be considered as discernable.

In terms of bar lines, as shown in FIG. 8B, the determination can bebased on the following formulas.

${{AverageBlack} = \frac{{\sum{Pixel}_{1}} + {\sum{Pixel}_{3}}}{{\sum L_{1}} + {\sum L_{3}}}},{and}$${AverageWhite} = \frac{\sum{Pixel}_{2}}{\sum L_{2}}$

where ΣPixel represents the sum of the intensity values of each pixel inthe particular region of interest, and ΣL represents the actual numberof pixels in the particular region of interest.

Thus, under the contrast adjusted sinusoidal approach, if

$\frac{AverageBlack}{AverageWhite}$

is less than 0.8673, then the bars or lines are considered to bediscernable. The formulation for discernable spokes follows a similarcalculation.

FIG. 8B illustrates two bars of a convolved plaid type resolution targetand FIG. 8C illustrates two rays of a convolved resolution spoke. Asshown by the arrows in FIG. 8B, it is possible to consider any portionalong the length of the resolution bars, when calculating the contrastratio. However, as illustrated by the arrows in FIG. 8C, with aresolution spoke the resolution can change along a radial direction. Inother words, the contrast ratio at one resolution radius may bedifferent from the contrast ratio at another resolution radius.Resolution rings located toward the center of the resolution spoke areless likely to provide a discernable contrast ratio, when compared toresolution rings toward the outer perimeter of the resolution spoke.

Calibration of Resolution Rings and Calculation of Acuity

The resolution rings can correspond to the radius at which the convolvedresolution spokes remain discernable, and beyond which the spokes are nolonger discernable. Determination of the resolution rings may depend onthe angular spacing of the spokes and the contrast of the resolutiontarget. As noted above, the Rayleigh criterion can be used to determinethe smallest resolution ring that can still distinguish the resolutionspoke, and thereby provide the resolution of the optical system. Theresolution can then be converted to optical acuity in Snellen format as20/20 plus number of letters, or in logMAR format, for example.

Several approaches can be used when determining and calibrating theresolution rings of a convolved resolution spoke. In a first approach,determination of the resolution ring can be accomplished using a 0.5 mmdiameter pupil, or aperture size. The Airy disk radius can be calculatedwith the formula r=1.22λ/D, where λ is the central wavelength of whitelight, and D is the diameter of the pupil. The disk radius in units ofradians can be calculated in terms of arc minutes as

r=1.22(0.55*180*60)/(0.5*1000*π)=4.613′,

which corresponds to the radius of the first dark portion of the disk,where λ is 0.55 μm. The ration 360/2π can be used to convert radians todegrees, and the ratio 60/1 can be used to convert degrees to arcminutes. This disk radius corresponds to about 33 pixels, when using a512 frame size. Different frame sizes may have different calibrationfactors.

Based on these calculations, 1′ (one arc minute) is equal to 33/4.613,or about 7.153 pixels. In this first approach, the resolution is pupilsize dependent. The arc length of each spoke at a normalized radius canbe calculated with the following formula.

arc length=2πr/θ=360° r/x°

Thus,

x/(360*2π*256 pixels*r)=7.153 pixels (for 20/20); and

r=(7.153*360)/(2πx*256)=0.1067

Consequently, the resolution radius for 20/20 acuity is determined to be0.1067. Table 1 illustrates the various resolution radius valuescorresponding to the Snellen acuity values, based on this first approachto calibrating the resolution rings.

TABLE 1 Acuity 20/10 20/20 20/40 20/80 20/160 r 0.053 0.1067 0.213 0.4270.854

Table 1 corresponds to the resolution rings shown in FIGS. 10A-E, wheredifferent resolution radius values correspond to different opticalacuity measure. Other approaches can be used to calibrate the resolutionrings based on this first approach.

For example, a second approach to calibration of the resolution ringsinvolves introducing a small amount of focusing error to the resolutionspoke to observe the effect of contrast reversal. Contrast reversalrefers to the phenomenon where the appearance of a single spokealternates between dark and light, as seen in FIGS. 9A and 9B. FIG. 9Ashows the contrast reversal with 0.25D focusing error for a 6 mm pupilwith 6° spacing in the resolution spoke. FIG. 913 shows the contrastreversal with 0.25D focusing error for a 6 mm pupil with 10° spacing inthe resolution spoke. FIG. 9C shows an optical transfer function of thedefocused resolution image of FIG. 6B. As illustrated in FIGS. 9B and9C, the 4 contrast reversals correspond to four places where the opticaltransfer function (OTF) changes sign.

With contrast reversal, it is possible to construct a resolution spokeand convolve it with only a small amount of defocus. With the secondapproach, on average, the real r is about 0.4 times as small as expectedwhen compared to the first approach. That means the resolution ringradius r from the first approach can be scaled by a factor of about 0.4to arrive at the resolution ring radius as derived by the secondapproach, as shown by the following formula which can estimate theresolution ring radius according to the second approach.

r=(7.153*0.4*360)/2πx*56 (modified formula)

The second column of Table 2 lists the spatial frequencies of the foursign reversals N in the optical transfer function (OTF) afterdiffraction-limited OTF calibration as shown in FIG. 6C. The spatialfrequency can be expressed in terms of cycles per degree, and can beused as a measure of resolution. The spatial frequencies of the secondcolumn can be used to calculate the arc minute values of the thirdcolumn, according the following formula

x=30/f

where x denotes arc minutes, and f denotes spatial frequency. Typically,20/20 acuity correlates to 30 cycles per degree, which also correspondsto one arc minute.

The fourth column contains resolution ring radius calculations based onthe modified formula as noted above, as calculated from the opticaltransfer function. This calculation involves considering the pupil sizeas 1, and normalizing the resolution ring radius. The fifth columncontains resolution rings radius estimates based on visual inspection ofthe contrast reversal in the resolution spoke as shown in FIG. 6B. Thefifth column is the ratio of the ring at reversal, versus the overallsize of the resolution target.

TABLE 2 Table 2. Spatial frequencies during sign reversal in the opticaltransfer function (OTF) corresponding to the radius of the resolutionrings at the contrast reversal in the resolution spoke. N Freq (cpd) Arcminute r real 1 23.0 (+ to −) 0.767 0.102 0.06 2 33.5 (− to +) 1.120.156 0.16 3 54.5 (+ to −) 1.82 0.273 0.27 4 101.6 (− to +)  3.39 0.3910.40

A third approach to calibration involves using different pupil sizes toconstruct different point spread functions (PSFs) to determine theresolution radius r of the individual pupil sizes. This approach can bebased on a diffraction limited case having no wavefront aberration.Table 3 shows the calculated resolution radius r corresponding tovarious pupil sizes. Here, the scaling factor is 0.6 as compared to thefirst approach.

TABLE 3 (diffraction limited case) No. pupil Airy disk resolution rratio ratio/0.1067 1 0.25 mm 9.226′ 0.58 0.063 0.59 2 0.5 mm 4.613′ 0.280.061 0.57 3 1 mm 2.306′ 0.14 0.061 0.57 4 2 mm 1.153′ 0.06 0.052 0.49

The Airy disk radius of the third column, in terms of arc minutes, canbe calculated from the second column according to the formula r=1.22λ/D,where D is the pupil diameter. The resolution r of the fourth column canbe based on a visual inspection of the convolved target. For example, asshown in FIG. 19, and described in the second row in Table 3, for a 0.5mm pupil, the resolution radius r is estimated at 0.28. The ratio of thefifth column can be calculated by dividing the resolution r of thefourth column by the radius of the Airy disk as indicated in the thirdcolumn. This ratio can divided by 0.1067, which is the resolution radiusat 20/20 Snellen acuity, as noted above in Table 3, and the result isshown in the sixth column. The calibration factor can then be based onthe values in the sixth column, which are approximately 0.6.

It may be desirable to average of 0.4 from the second approach, and 0.6from the third approach, to arrive at a calibration factor of 0.5.Hence, the resolution radius can be calculated as

r=(7.153*0.5*360)/(2πx*256)=(7.153*360)/(2πy*256)

where y=2x is the spacing factor. In this case, y=30, so r=0.05336,which is about one half the originally estimated value of 0.1067.

After the calibration, the resolution ring for a particular resolutionspoke (15° spacing) is shown in FIGS. 10A-E. FIG. 10A illustrates aresolution spoke having a resolution ring corresponding to an opticalacuity of 20/10. FIGS. 10B-10E illustrate resolution spokes havingresolution rings corresponding to optical acuities of 20/20, 20/40,20/80, and 20/160 respectively. Therefore, the radius of the resolutionring for 20/20 acuity can be represented by the following generalformula.

${r = \frac{360\; m}{4\; \pi \; {xd}}},$

where m is the pixel resolution per arc minute for thediffraction-limited PSF, x is the spoke spacing in degrees and d is thetotal number of pixels of the image frame. The image frame here is512×512 pixels. The resolution spoke, the PSF, and the convolved imagecan all have a frame dimension of 512×512 pixels.

Typically, a larger pupil will have a smaller point spread function, andvice versa. For example, if the pupil diameter is less than 2 mm, thediffraction limited point spread function may already be large enough,and there may be less need for corrective surgery. For eyes havinglarger pupils, higher order aberrations may play a greater role.

FIG. 13 shows a convolved Archimedes spiral resolution target.Calculation of optical acuity can be based on the same principlesdiscussed above with respect to resolution spokes. Higher resolutionmeasures correspond to resolution rings located toward the inner areasof the spiral, whereas lower resolution measures correspond toresolution rings located toward the outer periphery of the spiral.

It will be appreciated that the PSF may not always be rotationallysymmetric, as is possible in cases of astigmatism or coma. In someinstances, it may be desirable to do averaging or a combination methodbased on vectors provided by a resolution spoke approach and anArchimedes spiral approach, as discussed above. Similarly, some eyes mayhave strong horizontal astigmatism, and the vertical acuity may bebetter than the horizontal acuity. By using resolution targets such asArchimedes spiral, it may be possible to capture the directional bias,as shown in FIG. 14.

FIGS. 16 and 17 illustrate tangential acuity and radial acuity, whichare further explained in Table 4.

TABLE 4 Direction Acuity/Resolution Measure concentric/circulartangential/torsional inward - outward radial

As shown in FIG. 18, the acuity evaluation methods discussed above inreference to resolution spokes can also be applied to Archimedes spiral,including pixel calculations and the like. Multiple wavefrontmeasurements may also provide benefits.

Readjustment for Centration

As discussed above, after the resolution spoke is convolved with thepoint spread function (PSF), and the resolution rings are determined.Rayleigh's criterion can be implemented to determine the optical acuity.Ideally, the point spread function will be exactly centered with respectto the center of the spoke, thus making determination of optical acuitya more straightforward process. In some cases, however, the point spreadfunction (PSF) may not be centered. In fact, certain Zernike polynomialterms have an x- or y-component. Accordingly, the point spread function(PSF) for certain eyes may have some degree of de-centration. Thisde-centration can dramatically affect the estimated optical acuity.Therefore, it may be desirable to re-center the point spread function.To readjust for centration, the following four approaches can be used.Two approaches involve the pupil plane, and two involve the imagingplane.

In a first centration approach involving the pupil plane, the averagewavefront tilt is calculated and then compensated for the tilt. Thisapproach can be implemented with the Zernike derivative or with thediscrete wavefront differential averages.

Denoting Z(r, θ) as Zernike polynomials, the derivative of the wavefrontW(r, θ) can be written as

$\frac{\partial{W\left( {r,\theta} \right)}}{\partial x} = {{\frac{\partial}{\partial x}{\sum\limits_{i = 1}^{N}{c_{i}{Z_{i}\left( {r,\theta} \right)}}}} = {\sum\limits_{i = 1}^{N}{c_{i}\frac{\partial{Z_{i}\left( {r,\theta} \right)}}{\partial x}}}}$$\frac{\partial{W\left( {r,\theta} \right)}}{\partial y} = {{\frac{\partial}{\partial y}{\sum\limits_{i = 1}^{N}{c_{i}{Z_{i}\left( {r,\theta} \right)}}}} = {\sum\limits_{i = 1}^{N}{c_{i}\frac{\partial{Z_{i}\left( {r,\theta} \right)}}{\partial y}}}}$

where the Zernike derivative can be derived analytically so that theaverage wavefront tilt in both x- and y-directions can be calculated.

In a second centration approach involving the pupil plane, the wavefrontderivative can be implemented as the average wavefront pixel differencebetween two neighboring pixels in either x- or y-direction, as shown inthe following equations.

${\frac{\partial{W\left( {r,\theta} \right)}}{\partial x} = {\frac{1}{n}{\sum\limits_{i}{\sum\limits_{j}\left( {W_{i,{j + 1}} - W_{i,j}} \right)}}}},\left( {r \leq 1} \right)$${\frac{\partial{W\left( {r,\theta} \right)}}{\partial y} = {\frac{1}{n}{\sum\limits_{i}{\sum\limits_{j}\left( {W_{{i + 1},j} - W_{i,j}} \right)}}}},\left( {r \leq 1} \right)$

The calculation can be done within the pupil area with n the totalnumber of pixels within the area.

A first imaging plane approach is based on the calculated center ofgravity of the point spread function (PSF). The center of gravity of PSFcan be implemented according to the following equation:

$a_{x} = {\frac{\int{\int{{{xi}\left( {x,y} \right)}{x}{y}}}}{\int{\int{{i\left( {x,y} \right)}{x}{y}}}} = \frac{\sum\limits_{i}{\sum\limits_{j}{jI}_{i,j}}}{\sum\limits_{i}{\sum\limits_{j}I_{i,j}}}}$$a_{y} = {\frac{\int{\int{{{yi}\left( {x,y} \right)}{x}{y}}}}{\int{\int{{i\left( {x,y} \right)}{x}{y}}}} = \frac{\sum\limits_{i}{\sum\limits_{j}{iI}_{i,j}}}{\sum\limits_{i}{\sum\limits_{j}I_{i,j}}}}$

where i(x,y) and l_(i,j) represents the point spread function infunctional and discrete representations, respectively. This approach canalso be referred to as pixel weighting.

In a second imaging plane approach, a blurred spoke, for example, can becross correlated with an input spoke. The cross correlation between theshifted blurred spoke and the input resolution spoke can be expressed as

c(a _(x) ,a _(y))=l(x,y)⊕i(x−a _(x) ,y−a _(y)),

where l(x,y) denotes the input resolution spoke, i(x,y) denotes theblurred resolution spoke, and ⊕ denotes a symbol for correlation. Thecorrelation function can provide an indication to what degree theblurred image is de-centered relative to the input image. A surfacesearch for the maximum value in the correlation function c(a_(x),a_(y))can give the needed re-centration shift. For example, a function having100×100 pixels provides a total of 10,000 pixel values. A surface searchcan determine the position of the highest or maximum value pixel amongthese. Accordingly, this approach can have one pixel accuracy.

Once the image shift is obtained, it is possible to implement theadjustment. A first way of implementing the adjustment is to shift thepoint spread function (PSF) directly. If the point spread function (PSF)is fairly spread, this approach may require necessary data discard andzero padding. A second way of implementing the adjustment is to modifythe wavefront tilts in the pupil plane to achieve the eventual shift inthe blurred resolution spoke. Once the centration is readjusted, thepoint spread function can be centered and the estimation of the opticalacuity can be reliable. FIGS. 11A and 11B shows a blurred resolutionspoke without and with centration readjustment, respectively.Re-centration adjustment appears to result in a sharper image. Theestimated optical quality for FIG. 11A is 0.87 logMAR, whereas theestimated optical quality for FIG. 11B is 0.48 logMAR.

Clinical Test Results

To test the effectiveness of this technique, the following four clinicaltest results may be useful for prediction: high contrast uncorrectedvisual acuity, low contrast uncorrected visual acuity, high contrastbest spectacle corrected visual acuity, and low contrast best spectaclecorrected visual acuity.

Wavefront measurements were taken from eleven eyes at one-year postsurgery from patients undergoing myopic LASIK surgery. Optical acuitymeasures for these eyes were predicted according the present invention.The predicted visual acuity is compared to the corresponding subjectivemeasurements with 100% contrast. FIG. 12 shows the correlation of themeasured UCLM versus the predicted UCLM for these eyes. The predictedUCLM is an average of predicted UCLM from typically 3 to 5 wavefrontmeasurements, with the standard deviation also shown in the figure. Thecorrelation variance between predicted and measured was observed to beabout 74%. Hence, for the first time the optical acuity of human eyescan be accurately measured objectively.

Many of these wavefronts were taken in a dim ambient lighting condition,where a pupil diameter may be, for example, about 6 mm. In contrast, avisual acuity test usually is clone in a slightly brighter lightingcondition, where a pupil diameter may be, for example, about 4.5 mm.Therefore, these results may reflect some discrepancy between thepredicted acuity and the measured acuity. Though this can be compensatedfor, it may be desirable to know the exact pupil size when the visualacuity test is taken. Based on this knowledge, the input wavefront mapcan be truncated to approximate the pupil size of the eye that underwentvisual acuity testing, thereby permitting a direct comparison, andallowing an accurate prediction or determination of optical acuity.Thus, a 6 mm pupil diameter could be truncated, and a 4.5 mm wavefrontportion could form the basis of the point spread function, and thesubsequent acuity evaluation method.

The present invention also provides systems for predicting an opticalacuity measure of an eye, as depicted in the procedural flowchart ofFIG. 15A, and related system diagrams of FIGS. 15B-E. As shown in FIG.15B, a system of the present invention can include a module thatmeasures aberrations, which can include a wavefront measurementsubmodule, a wavefront map submodule, and a point spread functionsubmodule. The system can also include a module that simulates imagingof a resolution target, and this module can include a resolution targetsubmodule, a convolution submodule, and an image submodule. The systemcan further include an acuity evaluation module, which can includeacuity calculation and prediction submodules. FIG. 15C illustrates thata system of the present invention can include a wavefront module, aconvolution module that can have a wavefront map submodule, a pointspread function submodule, a resolution target submodule, and aconvolution submodule. The system can also include an acuity evaluationmodule that can have an image submodule and an acuity submodule. Asdepicted in FIG. 15D, a system according to the present invention caninclude an optical measurement module, an image simulation module thataccepts a resolution target, and an acuity estimator module. FIG. 15Eillustrates that a system of the present invention can include a pointspread function module, an image module, and an acuity module. Thesystem may also include a resolution target input module. The system mayhave a wavefront measurement input module, and the system may have awavefront measurement module.

A system according to the present invention can have a module thatdetermines a point spread function based on a wavefront measurement ofan eye, a module that convolves a resolution target with the pointspread function to produce an image, and a module that predicts theoptical acuity measure of the eye based on the image. The system canalso include an input that accepts the wavefront measurement of the eye,as well as a module that determines the wavefront measurement of theeye.

Similarly, the present invention provides for a system that includes amodule that measures visual distortion induced by optical aberrations ofan eye of an individual to determine an imaging performance of the eye,a module that constructs an acuity measurement model by simulatingimaging performance of the eye for a resolution target, and a modulethat determines an estimated visual acuity of the eye using the acuitymeasurement model. The module that determines an estimated visual acuitymay operate such that the estimated acuity accurately correlates to anactual visual acuity of the eye.

Evaluation Output

The approaches of the present invention also provide for the generationof an evaluation output for one or more eyes. An evaluation output mayalso be used to make a prediction of the outcome of an optical treatmentprocedure before the treatment is administered, or to evaluate theoutcome of an optical treatment procedure after the treatment isadministered.

In one embodiment, the evaluation output includes a visual acuityprediction for the eye. For example, Zernike polynomials from awavefront exam can be read into a StringGrid object and calculation of apoint spread function can be performed. An aperture, if smaller than thepupil size, can also be used to take the effect of pupil shrinkage. Thisapproach can be used to mitigate presbyopia, as further discussed inU.S. Provisional Patent Application No. 60/579,124, filed Jun. 10, 2004(Attorney Docket No. 018158-022230US), the entire contents of which areincorporated herein by reference. Nine eye chart letters (C, D, E, F, L,O, P, T, and Z) can be generated with fixed size corresponding todifferent visual acuity targets from 20/10 to 20/100 (e.g. 20/10, 20/12,20/15, 20/20, 20/25, 20/32, 20/40, 20/50, 20/64, 20/80, and 20/100). Byselecting a combination of an eye chart letter and a visual acuitytarget, this approach can perform a convolution of the PSF calculatedfrom the current wavefront exam with the selected eye chart letter. Byvisually determining whether the convolved letter is discernable it ispossible to predict a visual acuity for the eye based on the currentexam.

Aberrations

The present invention also provides for the correlation between opticalaberrations and visual acuity, such that it is possible to determine oridentify those aberrations which contribute to bad vision, thoseaberrations which contribute to good vision, and those aberrations whichdo not affect vision. Such determinations can be useful in designingablation profiles that induce aberrations where there were none,modifying existing aberrations, and/or deliberately not treating someaberrations that may contribute to good vision, wherein the aberrationscan include high order aberrations, for treating a vision condition in apatient. Such approaches can be used, for example to design a treatmentshape for presbyopia, based on the teachings found in U.S. Pat. Nos.6,280,435 and 6,663,619 to Odrich et al. (Attorney Docket Nos.018158-011110US and 018158-011120US), and U.S. Provisional PatentApplication No. 60/579,124, filed Jun. 10, 2004 (Attorney Docket No.018158-022230US), the entire contents of which are incorporated hereinby reference.

The approaches of the present invention can be implemented on a varietyof computer systems, including those with a 200 MHz CPU with 64 MBmemory, and typically will be coded in a computer language such as C orC++. Simulations have successfully been run on a laptop computer with a1.2 GHz CPU with 256 MB memory. The techniques of the present inventioncan also be implemented on faster and more robust computer systems.

The methods, systems, and devices of the present invention may beprovided in one or more kits for such use. The kits may include a systemfor predicting an optical acuity measure of an eye. Such a system caninclude a module that determines a point spread function based on awavefront measurement of an eye, a module that convolves a resolutiontarget with the point spread function to produce an image, and a modulethat predicts the optical acuity measure of the eye based on the image.The kit can also include instructions to use the system to predict anoptical acuity measure of an eye. Optionally, a kit may further includeany of the other system components or devices described in relation tothe present invention and any other materials or items relevant to thepresent invention. The instructions for use can set forth any of themethods as described above. Relatedly, the systems and devices of thepresent invention can be configured to carry out any of the method stepsdescribed herein.

While exemplary embodiments of the present invention have been describedin detail for clarity of understanding, a variety of modifications andchanges will be obvious to those of skill in the art. Hence, the scopeof the claims is limited solely by the appended claims.

1. A method for predicting an optical acuity measure of an opticalsystem of an eye, the method comprising: a) determining a point spreadfunction based on a wavefront measurement of an eye; b) centering thepoint spread function with respect to the center of the resolutiontarget; c) convolving a resolution target with the point spread functionto produce an image; and d) predicting the optical acuity measure of theoptical system of the eye based on the image.
 2. The method of claim 1,wherein the point spread function is centered based on compensation foran averaged wavefront tilt.
 3. The method of claim 2, wherein the pointspread function is centered based on the formulas$\frac{\partial{W\left( {r,\theta} \right)}}{\partial x} = {{\frac{\partial}{\partial x}{\sum\limits_{i = 1}^{N}{c_{i}{Z_{i}\left( {r,\theta} \right)}}}} = {\sum\limits_{i = 1}^{N}{c_{i}\frac{\partial{Z_{i}\left( {r,\theta} \right)}}{\partial x}}}}$$\frac{\partial{W\left( {r,\theta} \right)}}{\partial y} = {{\frac{\partial}{\partial y}{\sum\limits_{i = 1}^{N}{c_{i}{Z_{i}\left( {r,\theta} \right)}}}} = {\sum\limits_{i = 1}^{N}{c_{i}{\frac{\partial{Z_{i}\left( {r,\theta} \right)}}{\partial y}.}}}}$4. The method of claim 1, wherein the point spread function is centeredbased on implementation of a wavefront derivative as the averagewavefront pixel difference between two neighboring pixels in either thex- or y-direction.
 5. The method of claim 4, wherein the point spreadfunction is centered based on the following formulas${\frac{\partial{W\left( {r,\theta} \right)}}{\partial x} = {\frac{1}{n}{\sum\limits_{i}{\sum\limits_{j}\left( {W_{i,{j + 1}} - W_{i,j}} \right)}}}},\left( {r \leq 1} \right)$${\frac{\partial{W\left( {r,\theta} \right)}}{\partial y} = {\frac{1}{n}{\sum\limits_{i}{\sum\limits_{j}\left( {W_{{i + 1},j} - W_{i,j}} \right)}}}},{\left( {r \leq 1} \right).}$6. The method of claim 5, wherein the point spread function is centeredbased on a calculated center of gravity of the point spread function. 7.The method of claim 6, wherein the point spread function is centeredbased on the following formulas$a_{x} = {\frac{\int{\int{{{xi}\left( {x,y} \right)}{x}{y}}}}{\int{\int{{i\left( {x,y} \right)}{x}{y}}}} = \frac{\sum\limits_{i}{\sum\limits_{j}{jI}_{i,j}}}{\sum\limits_{i}{\sum\limits_{j}I_{i,j}}}}$$a_{y} = {\frac{\int{\int{{{yi}\left( {x,y} \right)}{x}{y}}}}{\int{\int{{i\left( {x,y} \right)}{x}{y}}}} = {\frac{\sum\limits_{i}{\sum\limits_{j}{iI}_{i,j}}}{\sum\limits_{i}{\sum\limits_{j}I_{i,j}}}.}}$8. The method of claim 1, wherein the point spread function is centeredbased on cross correlation between an input spoke and an output spoke.9. The method of claim 8, wherein the point spread function is centeredbased on the following formulac(a _(x) ,a _(y))=l(x,y)⊕i(x−a _(x) ,y−a _(y)).
 10. A method fordetermining an optical acuity measure of an optical system of an eye,the method comprising: a) determining a vision characteristic-modifiedpoint spread function based on a wavefront measurement of an eye; b)convolving a resolution target with the point spread function to producean image; and c) determining the optical acuity measure of the opticalsystem of the eye based on the image.
 11. The method of claim 10,wherein the resolution target is selected from the group consisting of asingle Snellen letter, a collection of Snellen letters, a plaid-typepattern, a resolution spoke, and an Archimedes spiral.
 12. The method ofclaim 10, wherein the contrast of the resolution target ranges fromabout 1% to about 100%.
 13. The method of claim 10, wherein the contrastof the resolution target ranges from about 10% to about 100%.
 14. Themethod of claim 10, wherein the resolution target is a resolution spokehaving an angular spacing that ranges from about 5° to about 30°. 15.The method of claim 10, wherein the resolution target is a resolutionspoke having an angular spacing of about 15°.
 16. The method of claim10, wherein the resolution target has a 512 pixel resolution.
 17. Themethod of claim 10, wherein the resolution target is a resolution spokehaving an angular spacing greater than about 30°, and having a 1024pixel resolution.
 18. The method of claim 10, wherein the resolutiontarget is a resolution spoke having an angular spacing of about 60, andhaving a 2048 pixel resolution.
 19. The method of claim 10, wherein anoptical resolution measure of the eye is based on the image, and theoptical acuity measure of the eye is based on the optical resolutionmeasure.
 20. The method of claim 19, wherein the optical resolutionmeasure of the eye is based on Rayleigh's criterion as applied to theimage.
 21. The method of claim 20, wherein the optical resolutionmeasure is based on a sinusoidal interpretation of the addition of twoAiry disks.
 22. The method of claim 21, wherein discernability in theoptical resolution measure is based on a contrast ratio of thesinusoidal interpretation.
 23. The method of claim 19, wherein theoptical acuity measure is represented in Snellen format.
 24. The methodof claim 19, wherein the optical acuity measure is represented in logMARformat.
 25. The method of claim 10, wherein the resolution target is aresolution spoke, and the optical acuity measure is calculated from aresolution ring calibration based on a 0.5 mm pupil diameter.
 26. Themethod of claim 10, wherein the resolution target is a resolution spoke,and the optical acuity measure is calculated from a resolution ringcalibration based on a defocused resolution spoke.
 27. The method ofclaim 10, wherein the resolution target is a resolution spoke, and theoptical acuity measure is based on a resolution ring calibration basedon aberration free cases of different pupil sizes ranging from about0.25 mm to about 2 mm.
 28. The method of claim 10, wherein the opticalsystem of the eye comprises a cornea and a lens of the eye.
 29. Themethod of claim 10, wherein the resolution target is represented by amodel.
 30. The method of claim 10, wherein the image is represented by amodel.
 31. A method for determining an optical acuity measure of anoptical system of an eye, the method comprising: a) determining a pointspread function based on a wavefront measurement of an eye; b) centeringthe point spread function with respect to the center of the resolutiontarget; c) convolving a resolution target with the point spread functionto produce an image; and d) determining the optical acuity measure ofthe optical system of the eye based on the image.
 32. The method ofclaim 31, wherein the point spread function is centered based oncompensation for an averaged wavefront tilt.
 33. The method of claim 32,wherein the point spread function is centered based on the formulas$\frac{\partial{W\left( {r,\theta} \right)}}{\partial x} = {{\frac{\partial}{\partial x}{\sum\limits_{i = 1}^{N}{c_{i}{Z_{i}\left( {r,\theta} \right)}}}} = {\sum\limits_{i = 1}^{N}{c_{i}\frac{\partial{Z_{i}\left( {r,\theta} \right)}}{\partial x}}}}$$\frac{\partial{W\left( {r,\theta} \right)}}{\partial y} = {{\frac{\partial}{\partial y}{\sum\limits_{i = 1}^{N}{c_{i}{Z_{i}\left( {r,\theta} \right)}}}} = {\sum\limits_{i = 1}^{N}{c_{i}{\frac{\partial{Z_{i}\left( {r,\theta} \right)}}{\partial y}.}}}}$34. The method of claim 31, wherein the point spread function iscentered based on implementation of a wavefront derivative as theaverage wavefront pixel difference between two neighboring pixels ineither the x- or y-direction.
 35. The method of claim 34, wherein thepoint spread function is centered based on the following formulas${\frac{\partial{W\left( {r,\theta} \right)}}{\partial x} = {\frac{1}{n}{\sum\limits_{i}{\sum\limits_{j}\left( {W_{i,{j + 1}} - W_{i,j}} \right)}}}},\left( {r \leq 1} \right)$${\frac{\partial{W\left( {r,\theta} \right)}}{\partial y} = {\frac{1}{n}{\sum\limits_{i}{\sum\limits_{j}\left( {W_{{i + 1},j} - W_{i,j}} \right)}}}},{\left( {r \leq 1} \right).}$36. The method of claim 31, wherein the point spread function iscentered based on a calculated center of gravity of the point spreadfunction.
 37. The method of claim 36, wherein the point spread functionis centered based on the following formulas$a_{x} = {\frac{\int{\int{{{xi}\left( {x,y} \right)}{x}{y}}}}{\int{\int{{i\left( {x,y} \right)}{x}{y}}}} = \frac{\sum\limits_{i}{\sum\limits_{j}{jI}_{i,j}}}{\sum\limits_{i}{\sum\limits_{j}I_{i,j}}}}$$a_{y} = {\frac{\int{\int{{{yi}\left( {x,y} \right)}{x}{y}}}}{\int{\int{{i\left( {x,y} \right)}{x}{y}}}} = {\frac{\sum\limits_{i}{\sum\limits_{j}{iI}_{i,j}}}{\sum\limits_{i}{\sum\limits_{j}I_{i,j}}}.}}$38. The method of claim 31, wherein the point spread function iscentered based on cross correlation between an input spoke and an outputspoke.
 39. The method of claim 38, wherein the point spread function iscentered based on the following formulac(a _(x) ,a _(y))=l(x,y)⊕i(x−a _(x) ,y−a _(y)).
 40. The method of claim31, wherein the optical acuity measure is determined by predicting themeasure.